Method and apparatus for calculating minimum valve lift for internal combustion engines

ABSTRACT

A controller calculates valve lift of intake and exhaust valves for a cylinder of an internal combustion engine. A first desired pressure ratio (P cyl /P int ) is selected to minimize induction pumping losses. Maximum cylinder demand is calculated. Intake valve lift is calculated by matching an effective flow capacity through at least one intake valve of the engine to the maximum cylinder demand. The intake valve is actuated based on the calculated intake valve lift. A second desired pressure ratio (P exh /P cyl ) for minimizing exhaust pumping losses is selected. Maximum cylinder demand is calculated. Exhaust valve lift is calculated by matching an effective flow capacity through at least one exhaust valve of the engine to the maximum cylinder demand. The exhaust valve is actuated based on the calculated exhaust valve lift.

FIELD OF THE INVENTION

[0001] The present invention relates to internal combustion engines, andmore particularly to a control system for calculating minimum valve liftfor an internal combustion engine.

BACKGROUND OF THE INVENTION

[0002] Intake valves control the air/fuel mixture into cylinders of aninternal combustion engine. Exhaust valves control gases exiting thecylinders of an internal combustion engine. Cams lobes on a camshaftpush against the valves to open the valves as the camshaft rotates.Springs on the valves return the valves to a closed position. Thetiming, duration and degree of the opening or “valve lift” of the valvesimpacts the performance of the engine.

[0003] As the camshaft spins, the cam lobes open and close the intakeand exhaust valves in time with the motion of the piston. There is adirect relationship between the shape of the cam lobes and the way thatthe engine performs at different speeds. When running at low speeds, thecam lobes should ideally be shaped to open as the piston starts movingdownward in the intake stroke. The intake valve closes as the pistonbottoms out and then, following compression combustion and expansionstrokes, the exhaust valve opens. The exhaust valve closes as the pistoncompletes the exhaust stroke.

[0004] At higher RPMs, however, this configuration for the camshaftlobes does not work as well. If the engine is running at 4,000 RPM, thevalves are opening and closing 33 times every second. At this speed, thepiston is moving very quickly. The air/fuel mixture rushing into thecylinder is also moving very quickly. When the intake valve opens andthe piston starts the intake stroke, the air/fuel mixture in the intakerunner starts to accelerate into the cylinder. By the time that thepiston reaches the bottom of its intake stroke, the air/fuel is movingat a high speed. If the intake valve is shut quickly, all of theair/fuel stops and does not enter the cylinder. By leaving the intakevalve open a little longer, the momentum of the fast-moving air/fuelcontinues to force air/fuel into the cylinder as the piston starts itscompression stroke. The faster the engine goes, the faster the air/fuelmoves and the longer the intake valve should stay open. The valve shouldalso be opened wider at higher speeds. This parameter, called valvelift, is governed by the cam lobe profile.

[0005] VTEC (Variable Valve Timing and Lift Electronic Control) by Hondais an electronic and mechanical system that allows the engine to havemultiple camshafts. VTEC engines have an extra intake cam lobe with arocker that follows the extra intake cam profile. The profile on theextra intake cam keeps the intake valve open longer than the other camprofile. At low engine speeds, the valves move in accordance with thestandard cam profile and the extra rocker is not connected to anyvalves. At high engine speeds, a pin locks the extra rocker to the twostandard rockers that activate the two intake valves.

[0006] Other engines phase the valve timing. This does not change thevalve duration; instead, the entire valve event is advanced or retarded.This is done by rotating the camshaft ahead a few degrees. If the intakevalves normally open at 10 degrees before top dead center (TDC) andclose at 190 degrees after TDC, the total duration is 200 degrees. Theopening and closing times are shifted using a mechanism that rotates thecam. For example, the valve might open at 10 degrees after TDC and closeat 210 degrees after TDC. Closing the valve 20 degrees later improvesperformance. However, it would be better to increase the duration thatthe intake valve is open.

[0007] The camshafts on some Ferrari engines are cut with athree-dimensional profile that varies along the length of the cam lobe.At one end of the cam lobe is the least aggressive cam profile, and atthe other end is the most aggressive. The shape of the cam smoothlyblends these two profiles together. A mechanism can slide the wholecamshaft laterally so that the valve engages different parts of the cam.The shaft spins just like a regular camshaft, but by gradually slidingthe camshaft laterally as the engine speed and load increases, the valvetiming can be optimized.

[0008] Several engine manufacturers are experimenting with systems thatwould allow infinitely variable valve timing lift and duration. Forexample, each valve has an actuator. A computer controls the opening andclosing of the intake and exhaust valves. These engines do not need acamshaft. With this type of engine control system, the maximum engineperformance minimum emission output, maximum efficiency or some balancedcombination of all three can theoretically be provided at every enginespeed and load. The computer controller, however, must have an algorithmfor valve lift that balances the energy consumption of the valveactuation system with the optimum thermo-dynamics of the engine. Thecalculations must also be computationally feasible by an enginecontroller at the anticipated calculation rates.

SUMMARY OF THE INVENTION

[0009] A method and apparatus according to the invention commands valvelift of an intake valve for a cylinder of an internal combustion engine.A first desired pressure ratio (P_(cyl)/P_(int)) is selected for minimuminduction pumping losses. A maximum cylinder flow demand is calculated.Intake valve lift is calculated by matching the effective flow capacitythrough intake valves of the engine to the maximum cylinder demand. Theintake valve is actuated based on the calculated valve lift.

[0010] In another aspect of the invention, method and apparatusaccording to the invention commands valve lift of an exhaust valve for acylinder of an internal combustion engine. A second desired pressureratio (P_(exh)/P_(cyl)) for minimum exhaust pumping losses is selected.A maximum cylinder demand is calculated. Exhaust valve lift iscalculated by matching an effective flow capacity through the exhaustvalves of the engine to the maximum cylinder demand. The exhaust valveis actuated based on the calculated exhaust valve lift.

[0011] Further areas of applicability of the present invention willbecome apparent from the detailed description provided hereinafter. Itshould be understood that the detailed description and specificexamples, while indicating the preferred embodiment of the invention,are intended for purposes of illustration only and are not intended tolimit the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The present invention will become more fully understood from thedetailed description and the accompanying drawings, wherein:

[0013]FIG. 1 illustrates a cylinder with intake and exhaust valves;

[0014]FIG. 2 is a functional block diagram of a control system forcalculating intake and exhaust valve lift for an internal combustionengine;

[0015]FIGS. 3A and 3B are flowcharts illustrating steps for calculatingminimum intake and exhaust valve lift;

[0016]FIG. 4 is a graph showing intake valve curtain area dischargecoefficient as a function of intake valve lift;

[0017]FIG. 5 is a graph showing minimum intake valve lift and minimumintake valve lift to diameter ratio as a function of engine speed;

[0018]FIG. 6 is a graph showing exhaust valve curtain area dischargecoefficient as a function of exhaust valve lift; and

[0019]FIG. 7 is a graph showing minimum exhaust valve lift and exhaustvalve lift to diameter ratio as a function of engine speed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0020] The following description of the preferred embodiment(s) ismerely exemplary in nature and is in no way intended to limit theinvention, its application, or uses.

[0021] The energy consumption of variable lift valve actuationtechnologies increase with valve lift. The present invention minimizesvalve lift without sacrificing the benefits of flexible valve liftcontrol. Minimum valve lift calculations are generated using amodel-based engine control system for an engine equipped with a variablelift valve actuators.

[0022] Referring now to FIG. 1, a piston 10 and a cylinder 12 of aninternal combustion engine are shown. The cylinder 12 includes intakeand exhaust manifolds 16 and 18. One or more valve drivers 20 adjust thevalve lift of intake and exhaust valves 22 and 24. For example, thevalve driver 20 can include a solenoid, a motor, or any other devicethat can accurately adjust the valve lift of the valves 22 and 24. Ascan be appreciated, additional intake and exhaust valves may beprovided.

[0023] Referring now to FIG. 2, an engine control system 50 forcalculating minimum valve lift for the internal combustion engine isshown. The engine control system includes an engine controller 52 and avalve driver 54. The engine controller 52 is connected to an oxygensensor 60 that senses oxygen content in the exhaust gas. The ECM 52 isalso connected to a pedal position sensor 62 that generates a pedalposition signal based upon accelerator pedal position. A dilution demandsignal is generated by the engine controller 52 based on calibration.The engine controller 52 and the valve driver 54 may be integrated ifdesired.

[0024] The engine controller 52 outputs intake valve signals such asintake valve opening, intake valve duration, and intake valve lift tothe valve driver 54. The engine controller 52 also generates RPM andcrank position signals to the valve driver 54. The engine controller 52outputs exhaust signals such as exhaust lift, exhaust duration andexhaust valve open signals to the valve driver 54. The valve driver 54outputs intake valve position and exhaust valve position signals to theengine controller 52.

[0025] Referring now to FIG. 3A, steps for calculating minimum intakevalve lift are shown generally at 100. Control begins in step 102. Instep 104, the crank position with maximum piston speed is calculated orlooked up. The step 104 is a one time calculation that is based on fixedengine geometry and is typically 72° after top dead center (ATDC) formost engines. This value is not calculated in real time.

[0026] If the valve closes before the position of maximum speed asdetermined in step 105, the valve closure position is used in step 106.Otherwise, the position of maximum speed is used in step 107. In step108, the desired pressure ratio (P_(cyl)/P_(int)) for reduced inductionpumping losses is selected. The desired pressure ratio (P_(cyl)/P_(int))can come from a table that is based on calibration and will probably berelatively constant. For intake, the desired pressure ratio(P_(cyl)/P_(int)) will be approximately 0.90. For exhaust, the desiredpressure ratio (P_(exh)/P_(cyl)) will be approximately 0.95.

[0027] In step 109, the intake manifold temperature is sampled. In step112, the minimum intake valve lift is calculated. In step 114, controlends. Steps 109 to 112 are repeated for future calculations. Optionally,the intake manifold temperature is estimated.

[0028] Referring now to FIG. 3B, steps for calculating minimum exhaustvalve lift are shown generally at 120. Control begins in step 122. Instep 124, the crank position with maximum piston speed is calculated orlooked up. The step 124 is a one time calculation that is based on fixedengine geometry and is typically ≈72° after top dead center (ATDC) formost engines. This value is not calculated in real time.

[0029] If the valve closes before the position of maximum speed asdetermined in step 125, the valve closure position is used in step 126.Otherwise, the position of maximum speed is used in step 127. In step128, the desired pressure ratio for reduced exhaust pumping losses isselected. In step 129, the exhaust manifold temperature is sampled. Theexhaust manifold temperature can be an estimate or a sensor signal,which may be obtained from a dedicated sensor, from a table, a model orfrom an adjacent model of another system. In step 132, the minimum liftis calculated. In step 134, control ends. Steps 129 to 132 are repeatedfor future calculations. Optionally, the exhaust manifold temperature isestimated.

[0030] Because the energy consumption of valve actuation increases withvalve lift, it is desirable to minimize valve lift without sacrificingthe benefit provided by flexible valve control. The minimum liftrequired to significantly reduce engine pumping losses can be found bymatching the mass flow capacity through the engine valves to the demandof the swept cylinder volume. The cylinder mass flow demand is theproduct of bulk gas density, piston speed and piston area,$\begin{matrix}{{\overset{.}{m}}_{cyl} = {{\rho_{cyl}\frac{V}{t}} = {{\rho_{cyl}A_{p}S_{p}} = \frac{\pi \quad P_{cyl}B^{2}S_{p}}{4R_{cyl}T_{cyl}}}}} & (1)\end{matrix}$

[0031] where instantaneous piston speed is given by, $\begin{matrix}{S_{p} = {\frac{\pi \quad {SN}}{60}{{\sin (\theta)}\left\lbrack {1 + \frac{\cos (\theta)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}(\theta)}}}} \right\rbrack}}} & (2)\end{matrix}$

[0032] The mass flow rate into the cylinder through the effective intakevalve flow area is given by $\begin{matrix}{{\overset{.}{m}}_{v,{int}} = {\frac{P_{int}A_{{eff},{int}}}{\sqrt{R_{int}T_{int}}}\psi_{int}}} & \left( {3a} \right) \\{where} & \quad \\{\psi_{int} = {{\left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}\quad {if}\quad \frac{P_{cyl}}{P_{int}}} > \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{\gamma - 1}}}} & \left( {4a} \right)\end{matrix}$

[0033] such that the flow is not choked. The effective flow area is theproduct of the discharge coefficient and valve curtain area,

A_(eff,int) =πC _(D,int) D _(n,int) n _(v,int) L _(int)  (5a)

[0034] Pumping loss is minimized when the effective flow area provides amass flow rate that meets the maximum cylinder demand at a pressureratio close to unity. The maximum demand occurs when the piston speed isa maximum. The crank position at which the piston speed is a maximum, θS_(p,max) , must be determined iteratively, but is constant for a givenratio of connecting rod length to stroke.

[0035] To find the maximum piston speed, set piston acceleration tozero,${\left( \frac{V}{t} \right)_{\max}\quad {occurs}\quad {when}\quad \frac{^{2}V}{t^{2}}} = 0$

[0036] Zero piston acceleration is given by,${{{\sin^{2}\left( \theta_{S_{p,\max}} \right)}\left\lbrack \frac{\frac{\cos^{2}\left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}} - \sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}} \right\rbrack} + {{\cos \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}} = 0$

[0037] or an alternative simplified form${{{\sin^{2}\left( \theta_{S_{p,\max}} \right)}\left\lbrack \frac{1 - \left( \frac{2l}{S} \right)^{2}}{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\theta_{S_{p,\max}}}} \right\rbrack} + {{\cos \left( \theta_{S_{p,\max}} \right)}\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}} + {\cos^{2}\left( \theta_{S_{p,\max}} \right)}} = 0$

[0038] which must be solved iteratively for θ_(S) _(p,max) .

[0039] If the engine valve closes prior to θ_(S) _(p,max) , then thepiston speed upon valve closure, θ_(VC), should be used. Equating themass flow rate through the valve to the maximum cylinder demand andsubstituting equations (1), (2), (3a), and (5a), $\begin{matrix}{\frac{\pi \quad C_{D,{int}}D_{v,{int}}n_{v,{int}}L_{int}P_{int}\psi_{int}}{\sqrt{R_{int}T_{int}}} = {\frac{\pi^{2}P_{cyl}B^{2}{SN}}{240R_{cyl}T_{cyl}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}} & (6)\end{matrix}$

[0040] Solving equation (6) for intake valve lift, $\begin{matrix}{L_{int} = {\frac{\pi \quad P_{cyl}B^{2}{SN}\sqrt{R_{int}T_{int}}}{240R_{cyl}T_{cyl}P_{int}C_{D,{int}}D_{v,{int}}n_{v,{int}}\psi_{int}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}} & (7)\end{matrix}$

[0041] Assuming that the cylinder bulk gas temperature is relativelyconstant during the high flow portion of the induction process, equation(7) indicates that engine speed is the only operating parameter thatdetermines the minimum required intake valve lift.

[0042] Define a constant, c_(int), as $\begin{matrix}{c_{int} = {{C_{D,{int}}L_{int}} = {\frac{\pi \quad P_{cyl}B^{2}{SN}\sqrt{R_{int}T_{int}}}{240R_{cyl}T_{cyl}P_{int}D_{v,{int}}n_{v,{int}}\psi_{int}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}}} & (8)\end{matrix}$

[0043] If the curtain area discharge coefficient can be described by apiecewise linear function of lift, C_(D,int)=b_(int)+a_(int)L_(int),equation (8) can be rewritten as,

c _(int) =C _(D,int) L _(int)=(b _(int) +a _(int) L _(int))L _(int) =b_(int) L _(int) +a _(int) L _(int) ²  (9)

[0044] Solving equation (9) for lift using the quadratic formula,$\begin{matrix}{L_{int} = \frac{{- b_{int}} \pm \sqrt{b_{int}^{2} + {4a_{int}c_{int}}}}{2a_{int}}} & (10)\end{matrix}$

[0045] For mass discharge from the cylinder during the exhaust process,equations (3a) and (4a) can be rewritten as, $\begin{matrix}{{\overset{.}{m}}_{v,{exh}} = {\frac{P_{cyl}A_{{eff},{exh}}}{\sqrt{R_{cyl}T_{cyl}}}\psi_{exh}}} & \left( {3b} \right) \\{where} & \quad \\{\psi_{exh} = {{\left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}\quad {if}\quad \frac{P_{exh}}{P_{cyl}}} > \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{\gamma - 1}}}} & \left( {4b} \right)\end{matrix}$

[0046] and equation (5a) can be written as,

A _(eff,exh) =πC _(D,exh) D _(v,exh) n _(v,exh) L _(exh)  (5b)

[0047] Equating the mass flow rate through the exhaust valve to themaximum cylinder demand and substituting equations (1), (2), (3b), and(5b), $\begin{matrix}{\frac{\pi \quad C_{D,{exh}}D_{v,{exh}}n_{v,{exh}}L_{exh}P_{cyl}\psi_{exh}}{\sqrt{R_{cyl}T_{cyl}}} = {\frac{\pi^{2}P_{cyl}B^{2}{SN}}{240R_{cyl}T_{cyl}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}} & (11)\end{matrix}$

[0048] Solving equation (11) for exhaust valve lift, $\begin{matrix}{L_{exh} = {\frac{\pi \quad B^{2}{SN}}{240C_{D,{exh}}D_{v,{exh}}n_{v,{exh}}\sqrt{R_{cyl}T_{cyl}}\psi_{exh}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}} & (12)\end{matrix}$

[0049] Equations (8) through (10) can be similarly applied to theexhaust valve to account for the dependence of discharge coefficient onvalve lift.

[0050] For an engine with a connecting rod length of, l=146.5 mm, and astroke of, S=94.6 mm, the position of maximum piston speed is θ_(S)_(p,max) =73.59°=1.284 rad, such that${{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack} = {{{\sin (73.6)}\left\lbrack {1 + \frac{\cos (73.6)}{\sqrt{\left\lbrack \frac{2\left( {146.5\quad {mm}} \right)}{94.6\quad {mm}} \right\rbrack^{2} - {\sin^{2}(73.6)}}}} \right\rbrack} = 1.051}$

[0051] If a pressure ratio of $\frac{P_{cyl}}{P_{int}} = 0.90$

[0052] g=0.90

[0053] sufficiently reduces induction pumping loss, the sub-criticalflow multiplier for air and fuel, γ=1.35, is given by,$\psi_{int} = {{\left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}} = {{(0.90)^{\frac{1}{1\quad 35}}\sqrt{\frac{2(1.35)}{1.35 - 1}\left\lbrack {1 - ({.90})^{\frac{{1\quad 35} - 1}{1\quad 35}}} \right\rbrack}} = 0.4217}}$

[0054] Assume the engine has a bore of, B=86 mm, two intake valves percylinder, n_(v,int)=2, each with a diameter of D_(v,int)=35.1 mm with anaverage low-lift discharge coefficient of C_(D,int)=0.63 and an intakemanifold temperature of T_(int)=298.15K. If the cylinder bulk gastemperature is relatively constant at T_(cyl)=350K during the inductionprocess, the minimum intake valve lift as a function of engine speed is,$L_{int} = {{\frac{{\pi (0.9)}\left( {86\quad {mm}} \right)^{2}\left( {94.6\quad {mm}} \right)\sqrt{\left( {0.276\quad \frac{{kN}\text{-}m}{{kg}\text{-}K}} \right)\left( {298.15\quad K} \right)\left( \frac{1000\quad N}{kN} \right)\left( \frac{{kg}\text{-}m}{N\text{-}s^{2}} \right)\left( \frac{1000\quad {mm}}{m} \right)^{2}}(1.051)}{240\left( {0.276\quad \frac{{kN}\text{-}m}{{kg}\text{-}K}} \right)\left( {350\quad K} \right)\left( \frac{1000\quad N}{kN} \right)\left( \frac{{kg}\text{-}m}{N\text{-}s^{2}} \right)\left( \frac{1000\quad {mm}}{m} \right)^{2}(0.63)\left( {35.1\quad {mm}} \right)\left( {2\quad \frac{valves}{cylinder}} \right)(0.4217)}\quad N} = {0.001379\quad N}}$

[0055] At 1300 rpm, the minimum intake lift required to significantlyreduce induction pumping loss is given by

L _(int)=0.001379(1300 rpm)=1.79 mm

[0056] If a pressure ratio of $\frac{P_{exh}}{P_{cyl}} = 0.95$

[0057] P1h=0.95

[0058] sufficiently reduces exhaust pumping loss, the sub-critical flowmultiplier is given by $\begin{matrix}{\psi_{exh} = {\left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}}} \\{= {{(0.95)^{\frac{1}{1\quad 29}}\sqrt{\frac{2(1.29)}{1.29 - 1}\left\lbrack {1 - ({.95})^{\frac{1.29 - 1}{1\quad 29}}} \right\rbrack}} = 0.3069}}\end{matrix}$

[0059] Assume the engine has two exhaust valves per cylinder,n_(v,exh)=2, each with a diameter of D_(v,exh)=30.1 mm with an averagelow-lift discharge coefficient of C_(D,exh)=0.703 and an average exhausttemperature of T_(cyl)=1000 K. The minimum exhaust valve lift as afunction of engine speed is$L_{exh} = {{\frac{{\pi \left( {86\quad {mm}} \right)}^{2}\left( {94.6\quad {mm}} \right)(1.051)}{240(0.703)\left( {30.1\quad {mm}} \right)\left( {2\quad \frac{valves}{cylinder}} \right)\sqrt{\left( {0.292\quad \frac{{kN}\text{-}m}{{kg}\text{-}K}} \right)\left( {1000\quad K} \right)\left( \frac{1000\quad N}{kN} \right)\left( \frac{{kg}\text{-}m}{N\text{-}s^{2}} \right)\left( \frac{1000\quad {mm}}{m} \right)^{2}}(0.3069)}\quad N} = {0.00137\quad N}}$

[0060] At 1300 rpm, the minimum lift required to significantly reduceexhaust pumping loss is given by,

L=0.001371(1300 rpm)=1.78 mm

[0061] Referring now to FIG. 4, the measured CD as a function of liftcharacterizes the flow characteristics of the specific engine geometry.This relationship is one input to the algorithm of the presentinvention.

[0062] Referring now to FIG. 5, an output of the algorithm of thepresent invention is shown. Engine speed is the primary operatingparameter upon which optimum valve lift depends. The effects of therelationship shown in FIGS. 4 and 6 do not become significant untilmoderate engine speeds such as approximately 3500 rpm. Otherwise,optimum lift is simply linear with speed. As a result, if N<the moderatespeed, optimum lift is approximately equal to C*N where C is a constant.If N>the moderate speed, optimum lift is approximately equal to C*N².

[0063] Those skilled in the art can now appreciate from the foregoingdescription that the broad teachings of the present invention can beimplemented in a variety of forms. Therefore, while this invention hasbeen described in connection with particular examples thereof, the truescope of the invention should not be so limited since othermodifications will become apparent to the skilled practitioner upon astudy of the drawings, the specification and the following claims.

1. A method for controlling valve lift of an intake valve for a cylinderof an internal combustion engine, comprising: selecting a first desiredpressure ratio (P_(cyl)/P_(int)) for induction pumping losses;calculating maximum cylinder demand; calculating intake valve lift bymatching an effective flow capacity through at least one intake valve ofsaid engine to said maximum cylinder demand; and actuating said intakevalve based on said calculated intake valve lift.
 2. The method of claim1 wherein said maximum cylinder demand occurs at a crank position whereone of maximum piston speed occurs and valve closure occurs.
 3. Themethod of claim 1 wherein said first desired pressure ratio is greaterthan 0.85 and less than or equal to 1.0.
 4. The method of claim 1wherein said first desired pressure ratio is approximately equal to 0.9.5. The method of claim 2 wherein said crank position at maximum pistonspeed is calculated by solving the following equation iteratively:${{{\sin^{2}\left( \theta_{S_{p,\max}} \right)}\left\lbrack \frac{\frac{\cos^{2}\left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}} - \sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}} \right\rbrack} + {{\cos \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}} = 0$

wherein S is stroke length, 1 is connecting rod length, and θ_(Sp,max)is said crank position at maximum piston speed.
 6. The method of claim 1wherein said calculated intake valve lift is calculated by solving:$L_{int} = {\frac{\pi \quad P_{cyl}B^{2}{SN}\sqrt{R_{int}T_{int}}}{240R_{cyl}T_{cyl}P_{int}C_{D,{int}}D_{v,{int}}n_{v,{int}}\psi_{int}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}$

wherein B is bore diameter, S is stroke length, N is engine speed,C_(D,int) is an intake discharge coefficient, T_(cyl) is cylinder bulkgas temperature, S is stroke, 1 is connecting rod length, D_(v,int) isintake valve diameter, R_(cyl) is a universal gas constant for intakegas, n_(v,int) is a number of intake valves per cylinder, θ_(Sp,max) issaid crank position at maximum piston speed, an in Ψ_(int) is:$\psi_{int} = {\left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}}$

wherein γ is a subcritical flow multiplier.
 7. A method for controllingvalve lift of an exhaust valve for a cylinder of an internal combustionengine, comprising: selecting a second desired pressure ratio(P_(exh)/P_(cyl)) for exhaust pumping losses; calculating maximumcylinder demand; calculating exhaust valve lift by matching an effectiveflow capacity through at least one exhaust valve of said engine to saidmaximum cylinder demand; and actuating said exhaust valve based on saidcalculated exhaust valve lift.
 8. The method of claim 7 wherein saidmaximum cylinder demand occurs at a crank position where one of maximumpiston speed occurs and valve closure occurs.
 9. The method of claim 7wherein said first desired pressure ratio is greater than 0.9 and lessthan or equal to 1.0.
 10. The method of claim 7 wherein said firstdesired pressure ratio is approximately equal to 0.95.
 11. The method ofclaim 8 wherein said crank position at maximum piston speed iscalculated by solving the following equation iteratively:${{{\sin^{2}\left( \theta_{S_{p,\max}} \right)}\left\lbrack \frac{\frac{\cos^{2}\left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}} - \sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}} \right\rbrack} + {{\cos \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}} = 0$

where S is stroke length, L is connecting rod length, and θ_(Sp,max) issaid crank position at maximum piston speed.
 12. The method of claim 7wherein said calculated valve lift is calculated by solving:$L_{exh} = {\frac{\pi \quad B^{2}{SN}}{240C_{D,{exh}}D_{v,{exh}}n_{v,{exh}}\sqrt{R_{cyl}T_{cyl}}\psi_{exh}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}$

wherein B is bore diameter, S is stroke length, N is engine speed,C_(D, exh) is a intake discharge coefficient, T_(cyl) is cylinder bulkgas temperature, S is stroke, l is connecting rod length, D_(v, exh) isexhaust valve diameter, R_(cyl) is a universal gas constant for exhaustgas, n_(v, exh) is a number of intake valves per cylinder, θ_(Sp,max) issaid crank position at maximum piston speed, and Ψ_(exh) is defined by:$\psi_{exh} = {\left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}}$

wherein γ is a subcritical flow multiplier.
 13. An engine control systemfor controlling valve lift of an intake valve for a cylinder of aninternal combustion engine, comprising: a controller that stores a firstdesired pressure ratio (P_(cyl)/P_(int)) for induction pumping losses,that calculates maximum cylinder demand, and that calculates intakevalve lift by matching an effective flow capacity through at least oneintake valve of said engine to said maximum cylinder demand; and a valveactuator that adjusts said intake valve based on said calculated valvelift.
 14. The engine control system of claim 13 wherein said maximumcylinder demand occurs at a crank position where one of maximum pistonspeed occurs and valve closure occurs.
 15. The engine control system ofclaim 13 wherein said first desired pressure ratio is greater than 0.85and less than or equal to 1.0.
 16. The engine control system of claim 13wherein said first desired pressure ratio is approximately equal to 0.9.17. The engine control system of claim 14 wherein said crank position atmaximum piston speed is calculated by solving the following equationiteratively:${{{\sin^{2}\left( \theta_{S_{p,\max}} \right)}\left\lbrack \frac{\frac{\cos^{2}\left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}} - \sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}} \right\rbrack} + {{\cos \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}} = 0$

wherein S is stroke length, 1 is connecting rod length, and θ_(Sp,max)is said crank position at maximum piston speed.
 18. The engine controlsystem of claim 13 wherein said calculated intake valve lift iscalculated by solving:$L_{int} = {\frac{\pi \quad P_{cyl}B^{2}{SN}\sqrt{R_{int}T_{int}}}{240R_{cyl}T_{cyl}P_{int}C_{D,{int}}D_{v,{int}}n_{v,{int}}\psi_{int}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}$

wherein B is bore diameter, S is stroke length, N is engine speed,C_(D, int) is a intake discharge coefficient, T_(cyl) is cylinder bulkgas temperature, S is stroke, l is connecting rod length, D_(v, int) isintake valve diameter, R_(cyl) is a universal gas constant for intakegas, n_(v, int) is a number of intake valves per cylinder, θ_(Sp,max) issaid crank position at maximum piston speed, and Ψ_(int) is:$\psi_{int} = {\left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{cyl}}{P_{int}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}}$

wherein γ is a subcritical flow multiplier.
 19. A engine control systemfor controlling valve lift of an exhaust valve for a cylinder of aninternal combustion engine, comprising: a controller that stores asecond desired pressure ratio (P_(exh)/P_(cyl)) for exhaust pumpinglosses, that calculates maximum cylinder demand, and that calculatesexhaust valve lift by matching an effective flow capacity through atleast one exhaust valve of said engine to said maximum cylinder demand;and an actuator that adjusts said exhaust valve based on said calculatedexhaust valve lift.
 20. The engine control system of claim 19 whereinsaid maximum cylinder demand occurs at a crank position where one ofmaximum piston speed occurs and valve closure occurs.
 21. The enginecontrol system of claim 19 wherein said first desired pressure ratio isgreater than 0.9 and less than or equal to 1.0.
 22. The engine controlsystem of claim 19 wherein said first desired pressure ratio isapproximately equal to 0.95.
 23. The engine control system of claim 20wherein said crank position at maximum piston speed is calculated bysolving the following equation iteratively:${{{\sin^{2}\left( \theta_{S_{p,\max}} \right)}\left\lbrack \frac{\frac{\cos^{2}\left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}} - \sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}} \right\rbrack} + {{\cos \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}} = 0$

where S is stroke length, l is connecting rod length, and θ_(Sp,max) issaid crank position at maximum piston speed.
 24. The engine controlsystem of claim 20 wherein said calculated valve lift is calculated bysolving:$L_{exh} = {\frac{\pi \quad B^{2}{SN}}{240C_{D,{exh}}D_{v,{exh}}n_{v,{exh}}\sqrt{R_{cyl}T_{cyl}}\psi_{exh}}{{\sin \left( \theta_{S_{p,\max}} \right)}\left\lbrack {1 + \frac{\cos \left( \theta_{S_{p,\max}} \right)}{\sqrt{\left( \frac{2l}{S} \right)^{2} - {\sin^{2}\left( \theta_{S_{p,\max}} \right)}}}} \right\rbrack}}$

wherein B is bore diameter, S is stroke length, N is engine speed,C_(D, exh) is a intake discharge coefficient, T_(cyl) is cylinder bulkgas temperature, S is stroke, l is connecting rod length, D_(v, exh) isexhaust valve diameter, R_(cyl) is a universal gas constant for exhaustgas, n_(v, exh) is a number of intake valves per cylinder, θ_(Sp,max) issaid crank position at maximum piston speed, and Ψ_(exh) is defined by:$\psi_{exh} = {\left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{1}{\gamma}}\sqrt{\frac{2\quad \gamma}{\gamma - 1}\left\lbrack {1 - \left( \frac{P_{exh}}{P_{cyl}} \right)^{\frac{\gamma - 1}{\gamma}}} \right\rbrack}}$

wherein γ is a subcritical flow multiplier.